1(1) The boiling point of TiF4 is 284 C. At that T, fHc = 1639 kJ mole
–1 and
fHv = 1551 kJ mole
–1. The molecule does not decompose during
evaporation. (a) Find out the enthalpy change vH and the fraction of this
energy that goes into pV. (b) Find out the equation for pv (Pa) with T (K)
as the only unknown. (c) What is pv at 30 C? (d) What is the TiF4
effusion rate at 30 C from an ideal Knudsen cell having a 1 mm-diameter
orifice? (5 + 2 + 5 + 3 + 5 points)
Homework 2
(Chapter 3 Evaporation, total points: 100 points)
(2) Water has a vH of 44 kJ mol
‒1, which can be approximated to be
independent of temperature. The boiling point of water is 100 °C. The
relative humidity, which is usually expressed as a percentage, is defined
as the ratio of the partial pressure of water in air to the saturated vapor
pressure of water at a given temperature. If the relative humidity at a city
is 80% at 30 °C, please calculate the partial pressure of water vapor in the
air at this city. (12 + 4 + 4 points)
2(3) A flat, 30 cm-diameter substrate is
situated with its center along the axis
of a Knudsen-cell orifice and 15 cm
away from it. The substrate is tilted
30 from being perpendicular to the
axis. Assuming that all material
arriving at the substrate condenses on
it, by what percentages do the
deposition rates at the lowest and
highest points on the substrate differ
from the rate at the center of the
substrate? (10 + 10 points)
3(4) (a) A light ray is traveling from water into glass. When the incidence
angle is 50.82, the reflected light is linearly polarized. If the refractive
index of water is 1.333, what is the refractive index of glass? What is the
Brewster’s angle when the light ray is traveling from glass into water? (b)
If the light ray is traveling from glass into water at an incidence angle of
65°, please find out the phase changes ϕr, and ϕr,|| upon reflection
according to the discussion on the lecture slides. You can self-check your
results according to the plots shown on Slide 78 of Chapter 3. (5 + 5 + 5 +
5 points)
(5) Consider a thin film coating of thickness d on an object (see the figure on
next page). If the incident wave has an amplitude of A0, then we have the
following amplitudes of various reflected and transmitted waves based on
the definitions of the reflection and transmission coefficients,
,
32
32
232
nn
nn
rr



212321231203
21231202
1201
trrrtAA
trtAA
rAA



23212321231203
2321231202
231201
trrrrtAC
trrtAC
ttAC



and so on. Assume that n1 < n2 < n3 and normal incidence. The phase
change in traversing the coating thickness is  = (2/)n2d in which  is
the free-space wavelength. The wave has to be multiplied by exp(j) to
account for this phase difference. The reflection and transmission
coefficients are given by
,21
21
21
121 r
nn
nn
rr 


 ,
2
21
1
121
nn
n
tt


,
2
21
2
212
nn
n
tt


32
2
233
2
nn
n
tt


4
5Please show the expressions
below. (10 + 10 points)
 



2
21
2
21
1
2
21
1
21
1
0
reflected
1 j
j
k
kj
err
err
err
r
tt
r
A
A
r






 
 




2
21
2
21
21
31
1
2
21
21
31
0
dtransmitte
1 j
jj
k
kj
j
err
err
rr
ett
err
rr
ett
A
C
t












 
The transmission coefficient is
The reflection coefficient is
6Please submit your solutions by 11:30 pm on 12 October 2023
(Thursday) on Blackboard. In case you have difficulty in uploading your
solutions on Blackboard, please send your solutions by email in time
to Mr. AN Ke (kan@phy.cuhk.edu.hk) or Ms. XIA Xinyue
(xyxia@phy.cuhk.edu.hk).